1. Extracting information from complex networks From the metabolism to collaboration networks Roger Guimerà Department of Chemical and Biological Engineering Northwestern University Bloomington, April 11th, 2005

2. High-throughput techniques in biology
Metabolic network
Protein interactions in fruit fly
Giot et al., Science (2003)

3. Large databases for critical infrastructures
World-wide airport network

4. Large databases for social networks
Collaborations in the Astronomical Journal
Collaborations in Econometrica

5. What do “statistical properties” tell us about the network?

6. What are the important cities in the world-wide airport network?
Most connected cities
Most central cities

7. Cartography of complex (metabolic) networks with L. A. N. Amaral

8. Cartography of complex (metabolic) networks
Modules One divides the system into “regions”
Roles One highlights important players

9. Real metabolic networks are extremely complex…

10. …and “regions” are not so well defined
Metabolic network of E. coli

11. One can define a quantitative measure of modularity
High modularity
Low modularity
Newman & Girvan, PRE (2003)

12. One can define a quantitative measure of modularity
Ds: expected fraction of links within module s, for a random partition of the nodes
ds: fraction of links within module s
Modularity of a partition: M = (ds – Ds)
Newman & Girvan, PRE (2003); Guimera, Sales-Pardo, Amaral, PRE (2004)

13. We use simulated annealing to obtain the partition with largest modularity

14. The new algorithm for module detection outperforms previous algorithms

15. Now we need to identify the role of each node

16. We define the within-module degree and the participation coefficient
Within-module relative degree
k: number of links of a node to other nodes in the same module
Within-module degree:
Participation coefficient
fis: fraction of links of node i in module s
Participation coefficient: Pi = fis 2

17. The within-module degree and the participation coefficient define the role of each node

18. We define seven different roles
Kinless hubs
Provincial
hubs
Connector
hubs
Hubs
Peripheral
Non-hub connectors
Kinless non-hubs
Non-hubs
Ultra-peripheral

19. The cartographic representation of the metabolic network of E. coli
Guimera & Amaral, Nature (2005)

20. The loss rate quantifies the importance of a role
Metabolite Role in Species A Role in Species B
A Ultra-peripheral Peripheral
B Connector hub Connector hub
C Ultra-peripheral LOST
D LOST Peripheral
...
Loss rate of role R: ploss(R) = p(lost | R)

21. Non-hub connectors are more conserved across species than provincial hubs
Comparison between 12 organisms:
4 archaea
4 bacteria
4 eukaryotes
Ultra-peripheral
Peripheral
Non-hub connectors
Provincial hubs
Connector hubs

22. Different networks have different role structures
1 – Ultra-peripheral
2 – Peripheral
3 – Non-hub connectors
5 – Provincial hubs
6 – Connector hubs

23. Collaboration networks: Team assembly, network structure, and performance with B. Uzzi, J. Spiro, and L. A. N. Amaral

24. Different collaboration networks have different properties
Different networks have different properties: average connectivity, S
What about non-scientific networks? Do they look very similar or very different?
Does any particular network structure spur creativity better than the others?
TRANSITION: In this case, we model how collaboration networks grow to answer this questions.
Collaborations in the Astronomical Journal
Collaborations in Econometrica

25. How do collaboration networks grow? How are teams assembled?
A model for collaboration network formation must specify what rules determine the participation of an individual in a team ? ? ?

26. Balancing expertise and diversity
But:
Need to incorporate new people
But:
It is easier to work with similar people and with former collaborators
Performance

27. Assembling a new team 1 4 3 2 5 2 1 5
1-p 3 4 p ?
Newcomers
Incumbents

28. Assembling a new team 1 4 3 2 5 2 1 5 3 4 4
Incumbents

29. ? Assembling a new team 1-p 4 p Newcomers Incumbents 1 4 3 2 5 2 1 5 3

30. Assembling a new team 1 4 3 2 5 4
Newcomers 6

31. ? Assembling a new team 1-p 4 p Newcomers Incumbents 6 1 4 3 2 5 2 1 5

32. Assembling a new team 1 4 3 2 5 2 1 5 3 4 4
Incumbents 6 ?

33. ? Assembling a new team 1-q q 4 Any incumbent Repeat collaboration 6 13 2 5 2 1 5 5
1-q 3 q 4 3 4
Any incumbent
Repeat collaboration 6 ?

34. Assembling a new team 1 4 3 2 5 5 3 4
Repeat collaboration 6 3

35. Assembling a new team 1 4 6 3 2 1 4 5 3 2 5 4 6 3

36. The structure of the network depends on the fraction of incumbents...
Guimera, Uzzi, Spiro & Amaral, Science (forthcoming 2005)

37. ...and on the tendency to repeat past collaborations
The size of the “invisible college” increases with the fraction of incumbents, p, and decreases with the tendency to repeat collaborations, q.

38. Most fields have very similar values of p and q

39. The fraction of incumbents is positively correlated with the impact factor of journals

40. The tendency to repeat collaborations is negatively correlated with the impact factor of journals

41. Conclusions
We need to go one step further in the analysis of complex networks, so that we can provide specific answers to specific problems.
Modules and roles give important information about the structure of a network and about the importance of each node.
Networks with different functions have different role structure.
In creative collaboration networks, the emergence of the invisible college and team performance are correlated to expertise and diversity (in a “network sense”), and there may be a universal optimum.

42. Acknowledgements
Marta Sales-Pardo, André A. Moreira, and Daniel B. Stouffer.
Fulbright Commission and Spanish Ministry of Education, Culture, and Sports.
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